Basic Math Examples

$\frac{5^{4 n} \cdot 25^{3 n}}{125^{2 n - 3}}$

Step 1

Rewrite $25$ as $5^{2}$ .

$\frac{5^{4 n} \cdot {(5^{2})}^{3 n}}{125^{2 n - 3}}$

Step 2

Multiply the exponents in ${(5^{2})}^{3 n}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5^{4 n} \cdot 5^{2 (3 n)}}{125^{2 n - 3}}$

Step 2.2

Multiply $3$ by $2$ .

$\frac{5^{4 n} \cdot 5^{6 n}}{125^{2 n - 3}}$

Step 3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5^{4 n + 6 n}}{125^{2 n - 3}}$

Step 4

Add $4 n$ and $6 n$ .

$\frac{5^{10 n}}{125^{2 n - 3}}$